<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
<meta http-equiv="X-UA-Compatible" content="IE=9"/>
<meta name="generator" content="Doxygen 1.8.13"/>
<meta name="viewport" content="width=device-width, initial-scale=1"/>
<title>Karamelo: material</title>
<link href="tabs.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="jquery.js"></script>
<script type="text/javascript" src="dynsections.js"></script>
<link href="navtree.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="resize.js"></script>
<script type="text/javascript" src="navtreedata.js"></script>
<script type="text/javascript" src="navtree.js"></script>
<script type="text/javascript">
  $(document).ready(initResizable);
</script>
<link href="search/search.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="search/searchdata.js"></script>
<script type="text/javascript" src="search/search.js"></script>
<script type="text/javascript">
  $(document).ready(function() { init_search(); });
</script>
<script type="text/x-mathjax-config">
  MathJax.Hub.Config({
    extensions: ["tex2jax.js", "TeX/AMSmath.js", "TeX/AMSsymbols.js"],
    jax: ["input/TeX","output/HTML-CSS"],
});
</script><script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.7/MathJax.js?config=TeX-MML-AM_CHTML/MathJax.js"></script>
<link href="doxygen.css" rel="stylesheet" type="text/css" />
<link href="karamelodoxy.css" rel="stylesheet" type="text/css">
<!--  -->
<script type="text/javascript" src="karamelo_navtree_hacks.js"></script>
</head>
<body>
<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
<div id="titlearea">
<table cellspacing="0" cellpadding="0">
 <tbody>
 <tr style="height: 56px;">
  <td id="projectlogo"><a href="http://www.karamelo.org"><img alt="Logo" src="Karamelo_logo.png"/></a></td>
  <td id="projectalign" style="padding-left: 0.5em;">
   <div id="projectname"><a href="http://www.karamelo.org">Karamelo</a>
   &#160;<span id="projectnumber">714599e9</span>
   </div>
   <div id="projectbrief">Parallel Material Point Method Simulator</div>
  </td>
   <td>        <div id="MSearchBox" class="MSearchBoxInactive">
        <span class="left">
          <img id="MSearchSelect" src="search/mag_sel.png"
               onmouseover="return searchBox.OnSearchSelectShow()"
               onmouseout="return searchBox.OnSearchSelectHide()"
               alt=""/>
          <input type="text" id="MSearchField" value="Search" accesskey="S"
               onfocus="searchBox.OnSearchFieldFocus(true)" 
               onblur="searchBox.OnSearchFieldFocus(false)" 
               onkeyup="searchBox.OnSearchFieldChange(event)"/>
          </span><span class="right">
            <a id="MSearchClose" href="javascript:searchBox.CloseResultsWindow()"><img id="MSearchCloseImg" border="0" src="search/close.png" alt=""/></a>
          </span>
        </div>
</td>
 </tr>
 </tbody>
</table>
</div>
<!-- end header part -->
<!-- Generated by Doxygen 1.8.13 -->
<script type="text/javascript">
var searchBox = new SearchBox("searchBox", "search",false,'Search');
</script>
</div><!-- top -->
<div id="side-nav" class="ui-resizable side-nav-resizable">
  <div id="nav-tree">
    <div id="nav-tree-contents">
      <div id="nav-sync" class="sync"></div>
    </div>
  </div>
  <div id="splitbar" style="-moz-user-select:none;" 
       class="ui-resizable-handle">
  </div>
</div>
<script type="text/javascript">
$(document).ready(function(){initNavTree('group__material.html','');});
</script>
<div id="doc-content">
<!-- window showing the filter options -->
<div id="MSearchSelectWindow"
     onmouseover="return searchBox.OnSearchSelectShow()"
     onmouseout="return searchBox.OnSearchSelectHide()"
     onkeydown="return searchBox.OnSearchSelectKey(event)">
</div>

<!-- iframe showing the search results (closed by default) -->
<div id="MSearchResultsWindow">
<iframe src="javascript:void(0)" frameborder="0" 
        name="MSearchResults" id="MSearchResults">
</iframe>
</div>

<div class="header">
  <div class="headertitle">
<div class="title">material</div>  </div>
</div><!--header-->
<div class="contents">
<h1><a class="anchor" id="Syntax"></a>
Syntax</h1>
<div class="fragment"><div class="line">material(material-ID, rigid)</div><div class="line">material(material-ID, linear, rho, E, nu, optional: damage-ID)</div><div class="line">material(material-ID, neo-hookean, rho, E, nu, optional: damage-ID)</div><div class="line">material(material-ID, eos-strength, eos-ID, strength-ID, optional: damage-ID, optional: temperature-ID)</div></div><!-- fragment --><ul>
<li>
material-ID: name of the material to be created. </li>
<li>
rho: density of the material. </li>
<li>
E: Young's modulus. </li>
<li>
nu: Poisson's ration. </li>
<li>
damage-ID: name of the damage law to be used (see Damage). </li>
<li>
temperature-ID: name of the temperature law to be used (see Temperature). </li>
<li>
eos-ID: name of <a class="el" href="classEOS.html">EOS</a> (Equation of State) to be used. </li>
<li>
strength-ID: name of hardening law to be used (see Strength). </li>
</ul>
<h1><a class="anchor" id="Examples"></a>
Examples</h1>
<div class="fragment"><div class="line">E        = 115</div><div class="line">nu       = 0.31</div><div class="line">rho      = 8.94e-06</div><div class="line">material(mat1, linear, rho, E, nu)</div></div><!-- fragment --><p> Defines a linear elastic material called 'mat1'. Its density is 8.94e-06, Poisson's ration 0.31 and Young's modulus 115.</p>
<h1><a class="anchor" id="Description"></a>
Description</h1>
<p>Four different kinds of materials are supported: </p><ul>
<li>
Rigid. The material does not deform. </li>
<li>
Linear, defined by their density, Young's modulus \(E\) and Poisson's ratio \(\nu\). In this case, the stress is directly related to the strain increment:<br />
 <p class="formulaDsp">
\begin{equation} \boldsymbol{\sigma} = 2G \Delta \boldsymbol{\varepsilon} + \lambda \text{tr}(\Delta \boldsymbol{\varepsilon}) \boldsymbol{I} \end{equation}
</p>
 where the shear modulus \(G\) and Lame parameter \(\lambda\) are obtained as follows: <p class="formulaDsp">
\begin{equation} G = \frac{E}{2 (1 + \nu)}\\ \lambda = \frac{E \nu}{(1 + \nu) (1 - 2 \nu)} \end{equation}
</p>
 </li>
<li>
Neo-Hookean, defined by their density, Young's modulus \(E\) and Poisson's ratio \(\nu\). In this model, the first Piola-Kirchhoff stress tensor is given by: <p class="formulaDsp">
\begin{equation} \boldsymbol{P} = G (\boldsymbol{F} - \boldsymbol{F}^{-T}) + \lambda \left( \ln J \right)\boldsymbol{F}^{-T} \end{equation}
</p>
 where \(J\) is the determinant of \(\boldsymbol{F}\).  </li>
<li>
<p class="startli">Elasto-plastic: defined by an equation of state (<a class="el" href="classEOS.html">EOS</a>) and a hardening law (Strength).</p>
<p>For all non-rigid materials, damage (Damage) is supported, to add allow for the use of a damage law, its ID, damage-ID, needs to be given.</p>
<p class="endli">Finally, for elasto-plastic materials, the increase of temperature coming from the plastic work can be talken into account using a temperature law (Temperature). </p>
</li>
</ul>
</div><!-- contents -->
</div><!-- doc-content -->
<!-- start footer part -->
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
  <ul>
    <li class="footer">Generated on Tue Jul 7 2020 22:31:23 for Karamelo by
    <a href="http://www.doxygen.org/index.html">
    <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.13 </li>
  </ul>
</div>
<!-- Matomo -->
<script type="text/javascript">
  var _paq = _paq || [];
  /* tracker methods like "setCustomDimension" should be called before "trackPageView" */
  _paq.push(['trackPageView']);
  _paq.push(['enableLinkTracking']);
  (function() {
    var u="//stats.sylphide-consulting.com/matomo/";
    _paq.push(['setTrackerUrl', u+'piwik.php']);
    _paq.push(['setSiteId', '20']);
    var d=document, g=d.createElement('script'), s=d.getElementsByTagName('script')[0];
    g.type='text/javascript'; g.async=true; g.defer=true; g.src=u+'piwik.js'; s.parentNode.insertBefore(g,s);
  })();
</script>
<noscript><p><img src="//stats.sylphide-consulting.com/matomo/piwik.php?idsite=20&rec=1" style="border:0;" alt="" /></p></noscript>
<!-- End Matomo Code -->
</body>
</html>
